$\dfrac{d}{dx}\left(x^{^{\scriptsize\dfrac{3}{4}}}\right)=$
Solution: The derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a fraction.) $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{^{\frac{3}{4}}}\right) \\\\ &=\dfrac{3}{4}x^{^{\frac{3}{4}-1}} \gray{\text{The power rule}} \\\\ &=\dfrac{3}{4}x^{^{-\frac{1}{4}}} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(x^{^{\frac{3}{4}}}\right)=\dfrac{3}{4}x^{^{-\frac{1}{4}}}$. This can also be written as $\dfrac{3}{4\sqrt[4]x}$ (all equivalent forms are accepted).